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With the type of posts you see on TV it's impossible to get the net absolutely straight on top because the posts will fall inward - there's something like 100 kg holding them in place, but they'll tilt if the string gets tight enough. If I had my maths hat on I'd have a go at working out the minimum possible dip for the given catenary and tension, but it's only 10 am...

(The posts at our club are sunk into the floor, so we can get our nets basically straight i.e. eight of inch or less.)

Even if you had solid, high-strength steel posts (and thick steel cables to take the tension), there would still be a few mm of deflection. Plus, you'd have to have a tennis-net style crank to apply the tension.

My club doesn't have posts which fit into the floor, so an inch is about the best we can achieve before the posts (with additional weight) start to slip inwards.

However, did play at a club in Denmark. They had a turnbuckle tensing a steel cable. They could achieve such a high tension that you could sit on it! Didn't look comfortable or safe, so didn't try it myself!

Kwun's answer is correct. It is necessary to have that 1 inch dip in the middle due to physics. The poles are required to be 5' 1", so when we go measure nets, we just measure the middle to be 5', the sides should already be 5' 1".